Question

select the correct answer.
the sum of two trinomials is 6x² - 5x + 4. if one of the trinomials is 4x² + 3x - 2, then what is the other trinomial?
10x² + 2x - 2
10x² + 8x - 6
2x² - 8x + 6
2x² - 2x + 2

Explanation:

Step1: Let the other trinomial be $A$.

We know that the sum of two trinomials is $6x^{2}-5x + 4$ and one trinomial is $4x^{2}+3x - 2$. So, $A+(4x^{2}+3x - 2)=6x^{2}-5x + 4$.

Step2: Solve for $A$.

$A=(6x^{2}-5x + 4)-(4x^{2}+3x - 2)$.

Step3: Distribute the negative sign.

$A = 6x^{2}-5x + 4-4x^{2}-3x + 2$.

Step4: Combine like - terms.

For the $x^{2}$ terms: $6x^{2}-4x^{2}=2x^{2}$.
For the $x$ terms: $-5x-3x=-8x$.
For the constant terms: $4 + 2=6$.
So, $A = 2x^{2}-8x + 6$.

Answer:

C. $2x^{2}-8x + 6$